Skip to main content

Sudoku technique

XY-Wing

Three two-candidate cells in a chain. You cannot tell which way any of them resolves, and it does not matter — one of the two wings is guaranteed to take the shared digit either way.

What an XY-Wing is

An XY-Wing is three cells, each with exactly two candidates, arranged so that a pivot cell holding X,Y can see one cell holding X,Z and another holding Y,Z.

The conclusion is that one of the two wings must be Z. The pivot is X or Y; if it is X the first wing cannot be, so it is Z; if it is Y the second wing is Z. Either way a Z appears in one of the wings, so any cell that sees both of them cannot be Z.

“See” means the ordinary Sudoku sense: sharing a row, a column or a box.

Why it feels different

Every technique before this one is about a single unit, or about one digit across the grid. The XY-Wing is the first that reasons about a chain — it takes a fact you do not know (which digit the pivot holds), splits it into cases, and finds something both cases agree on.

That is a genuinely different kind of argument, and it is the doorway into the harder techniques. Almost everything beyond it — XYZ-Wings, colouring, forcing chains — is the same move applied at greater length.

6
3
2
4
9
1
8
1
7
5
3
8
2
9
8
9
4
6
1
3
6
8
5
9
2
4
8
9
3
1
9
3
8
7
8
9
2
5
9
7
8
1
9
8
2
3

Step 1 of 5

A real position

A hard grid with candidates marked. Every simpler technique has been played out; what is left is cells with two candidates each and no obvious pair among them.

A real position from a generated puzzle. Every elimination shown here was checked against that puzzle's actual solution.

How to hunt one

Mark every cell with exactly two candidates. On a stalled hard board there are usually six to a dozen, and that is your entire search space.

Take each one as a pivot and look at the two-candidate cells it can see. You want two of them that share a digit with the pivot — a different one each — and share their remaining digit with each other. Then check for cells seeing both wings; if there are none, move on, because a pattern that eliminates nothing is not worth the time.

The one that looks the same but is not

If all three cells sit in the same unit you do not have an XY-Wing, you have a naked triple — which is stronger and easier to apply. The XY-Wing earns its keep precisely when the three cells are spread across different units and no simpler pattern connects them.

Where it sits

Reach for it after singles, pairs, and the box and line interactions have all been exhausted. On most boards that is far enough. Alongside the X-Wing and the Swordfish it covers essentially everything an expert grid will ask of you.

Other techniques

Try it on a real board

The free board on the home page has a notes mode, which is what every technique past hidden singles needs. Then take the same eye into a live match.